This may seem random but it is required by the game. This is not dependent of age of your Mountain. The only thing it depends on it is total playtime of the current Mountain.

Notes:
If your Mountain gets annihilated while idling, do NOT click "retry" but close out of the game. You will get your mountain back at the last made save. Also making backups of your save is a good idea. I've also heard reports of playtime for a save becoming bugged and not counting up. If this happens the only thing you can do is load an early save backup or start a new save. You will know if it is bugged by checking your save with a hex editor described in the next section.

Alternatively, this achievement can be obtained through save editing.

First, locate Mountain's save files.
On Windows, this should be located in the path:
On OSX i've heard it is located here:
On Linux/SteamOS i've heard it is located here:

Second, open the .sav files in a hex editor (such as the program HxD) until you open the one laid out exactly like this (this is an example save):
The size of this file is small, bytes in size.
This is the save that controls certain stats in the game, and what you are looking for is the total time played. The one that controls this is the hex:
In the third row, last 8 characters (or bytes). The game works in such a way that it converts the decimal of hours played into hexadecimal. Then it appends zeros to the end of this hexadecimal to make it a certain length. Ignoring the zeroes, 3e in hexadecimal converted to decimal is 62. To unlock the achievement, one can put any number over 987 in hexadecimal.
For example, replacing with will unlock the achievement!
In the end, the save looks like this.

Thanks to the developer of Mountain, David OReilly
And thanks to https://psteamcommunity.yuanyoumao.com/id/rei_onryou for investigating a few things